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# Measuring Solid Volume Help

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By — McGraw-Hill Professional
Updated on Apr 25, 2014

## Measuring Solid Volume

Suppose, in the preceding problem, that the object in question is irregular. How can we know that its volume is 45.3 cm 3 ? It would be easy to figure out the volume if the object were a perfect sphere or a perfect cube or a rectangular prism. Suppose, however, that it’s a knobby little thing?

Scientists have come up with a clever way of measuring the volumes of irregular solids: Immerse them in a liquid. First, measure the amount of liquid in a container (Fig. 10-2a). Then measure the amount of liquid that is displaced when the object is completely submerged. This will show up as an increase in the apparent amount of liquid in the container (see Fig. 10-2b). One milliliter (1 ml) of water happens to be exactly equal to 1 cm 3 , and any good chemist is bound to have a few containers marked off in milliliters. This is the way to do it, then, provided the solid does not dissolve in the liquid and that none of the liquid is absorbed into the solid.

Fig. 10-2 . Measuring the volume of a solid, ( a ) a container with liquid but without the sample; ( b ) a container with the sample totally submerged in the liquid.

## Specific Gravity Of Solids

Another important characteristic of a solid is its density relative to that of pure liquid water at 4°C (about 39°F). Water is at its most dense at this temperature and is assigned a relative density of 1. Substances with relative density greater than 1 will sink in pure water at 4°C, and substances with relative density less than 1 will float in pure water at 4°C. The relative density of a solid, defined in this way, is called the specific gravity . You often will see this abbreviated as sp gr. It is also known as relative density.

You certainly can think of substances whose specific gravity numbers are greater than 1. Examples include most rocks and virtually all metals. However, pumice, a volcanic rock that is filled with air pockets, floats on water. Most of the planets, their moons, and the asteroids and meteorites in our solar system have specific gravities greater than 1, with the exception of Saturn, which would float if a lake big enough could be found in which to test it!

Interestingly, water ice has specific gravity of less than 1, so it floats on liquid water. This property of ice is more significant than you might at first suppose. It allows fish to live underneath the frozen surfaces of lakes in the winter in the temperate and polar regions of the Earth because the layer of ice acts as an insulator against the cold atmosphere. If ice had specific gravity of greater than 1, it would sink to the bottoms of lakes during the winter months. This would leave the surfaces constantly exposed to temperatures below freezing, causing more and more of the water to freeze, until shallow lakes would become ice from the surface all the way to the bottom. In such an environment, all the fish would die during the winter because they wouldn’t be able to extract the oxygen they need from the solid ice, nor would they be able to swim around in order to feed themselves. It is difficult to say how life on Earth would have evolved if water ice had a specific gravity of greater than 1.

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